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Physical Review A

Prethermal discrete time crystal in driven-dissipative dipolar systems

Saptarshi Saha, Rangeet Bhattacharyya

Published Jan 11, 2024• 4 citations
Publisher

Abstract

Here we provide a theoretical framework to analyze discrete time-crystalline (DTC) phases in the dissipative dipolar systems subjected to a two-pulse excitation scheme. As a particular realization, we choose a quantum many-body system that exhibits prethermalization due to the presence of the quasiconserved quantities. The analysis uses a fluctuation-regulated quantum master equation, which captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the effects of such dissipation lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. We also obtain the lifetime of such a robust period-doubling response, a salient feature of the DTC phase, by varying several system parameters. Our results are in good agreement with the recent experimental findings in dipolar systems using nuclear magnetic resonance spectroscopy. Finally, we provide an estimate how the DTC performance degrades with temperature.

DOI
10.1103/physreva.109.012208

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Here we provide a theoretical framework to analyze discrete time-crystalline (DTC) phases in the dissipative dipolar systems subjected to a two-pulse excitation scheme. As a particular realization, we choose a quantum many-body system that exhibits prethermalization due to the presence of the quasiconserved quantities. The analysis uses a fluctuation-regulated quantum master equation, which captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the effects of such dissipation lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. We also obtain the lifetime of such a robust period-doubling response, a salient feature of the DTC phase, by varying several system parameters. Our results are in good agreement with the recent experimental findings in dipolar systems using nuclear magnetic resonance spectroscopy. Finally, we provide an estimate how the DTC performance degrades with temperature.
Here we provide a theoretical framework to analyze discrete time-crystalline phases (DTC) in open quantum many-body systems. As a particular realization, we choose a quantum many-body system that exhibits cascaded prethermalization . The analysis uses a fluctuation-regulated quantum master equation. The master equation captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the dissipators from the drive and the dipolar interactions lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. Our results are in good agreement with the experiments. Finally, we show and quantify how the DTC performance degrades with temperature.
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)NATUAS0028-083610.1038/nature21426]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.
Many-body quantum systems, under suitable conditions, exhibit time-translation symmetry breaking and settle in a discrete time crystalline (DTC) phase -- an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust subharmonic response. However, the DTC phase is fragile in the presence of environmental dissipation. Here, we propose and exemplify a DTC phase in a noninteracting system that owes its stability to environmental dissipation. The lifetime of this DTC is independent of initial conditions and the size of the system, though it depends on the frequency of the external driver. We experimentally demonstrate this realization of DTC using Nuclear Magnetic Resonance spectroscopy.
Recent experiments show that periodic drives on dipolar systems lead to long-lived prethermal states. These systems are weakly coupled to the environment and reach prethermal states on a timescale much shorter than the timescale for thermalization. Such nearly closed systems have previously been analyzed using Floquet formalism, which shows the emergence of a prethermal plateau. We use a fluctuation-regulated quantum master equation (FRQME) to describe these systems. In addition to the system-environment coupling, FRQME successfully captures the dissipative effect from the various local interactions in the system. Our investigation reveals a cascaded journey of the system to a final steady state. The cascade involves a set of prethermal or arrested states characterized by a set of quasiconserved quantities. We show that these prethermal states emerge in a timescale much shorter than the relaxation timescale. We also find and report the existence of a critical limit beyond which the prethermal plateau ceases to exist.
Prethermal discrete time crystals (DTCs) are a novel phase of periodically driven matter that exhibits robust subharmonic oscillations without requiring disorder. However, previous realizations of prethermal DTCs have relied on the presence of polarization, either spontaneous or induced. Here we introduce a class of prethermal DTCs termed ``unpolarized prethermal discrete time crystals'' (UPDTCs) that arise without any uniform or staggered polarization and propose an experiment to observe them in current trapped-ion quantum simulators. By studying a model of trapped ions using a quantum circuit simulator, we demonstrate that robust period-doubled dynamics can persist in the autocorrelation function of the staggered magnetization, even though its expectation value does not exhibit such dynamics. The period-doubled dynamics is not explained by the classical picture of flipping spins but by quantum fluctuations. We establish that UPDTCs are exponentially long-lived in the high-frequency driving regime, a hallmark of prethermalization. These results expand the known phenomenology and mechanism of prethermal time crystals and underscore the role of quantum effects in stabilizing novel nonequilibrium phases.
Abstract Periodically driven closed quantum many-body systems are known to exhibit prethermal or quasi-steady-state dynamics. In this work, we theoretically show that such prethermal phases can appear in the dynamics of a dipolar two-spin-1/2 system coupled to a heat bath if the cross terms between the drive and dipolar interactions are taken into consideration. To this end, we use our recently reported fluctuation-regulated quantum master equation (Chakrabarti A. and Bhattacharyya R., Phys. Rev. A 97 (2018) 063837), to show that the predicted dynamics can successfully explain the experimentally observed features of the transient and prethermal regime.